Cube root of 1728

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Intermediate

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A cube root of a number is a value that, when multiplied by itself three times, gives the original number. We write the cube root of a whole number like x = ∛x whereby, with x = 1728 specifically, we write the cube of 1728 as ∛1728. Cube roots come in handy to determine & prepare the apt dosage of medicine keeping BMI in mind.

What is the cube root of 1728?

We know that 1728 is a perfect cube so the cube root of 1728 will be 12. The cube root of 1728 is written as ∛1728 in radical form and “∛" sign is called the “radical” sign. In exponential form, it is written as (1728)^⅓

Finding the ∛1728

We can find the cube root of 1728, mainly through two methods:

i) Prime Factorization method.

ii) Subtraction method.

Cube root of 1728 by Prime Factorization method

Finding a cube root of 1728 through the Prime Factorization method involves determining the factor of 1728.

Step 1 — Find the prime factors of 1728.

So the prime factor of 1728 is 2x2x2x2x3x3x3x2x2

Step 2 — Group the factors of 1728 in a group of 3.

Step 3–We have 9 digits, which makes a set of 3 triplets. Make sure that the triplets are of the same digit.

Note: During Prime factorization, a pair of 2 digits is made in square roots whereas in a cube a triplet is made.

The cube root of 1728 can be written as ∛1728 = ∛(2x2x2)x(2x2x2)x(3x3x3) = 2x2x3 = 12

We can say that from the above simplifications and calculations, the cube root of 1728 is 12.

Cube root of 1728 by Subtraction method

The subtraction method involves subtracting successive numbers repeatedly.

Subtract the numbers 1,7,19,37,61,91,127,169,217,331,397…….. successively till we get a zero.

Subtracting the successive number method is based on the properties of cubes and the differences between consecutive cubes.

Here, the subtraction took place in 12 steps to reach zero.

We can figure out that the cube root of 1728 is 12.

Important Glossaries for Cube Root of 1728

Exponential form:It is a way of writing numbers that involve repeated multiplication.

Approximation:Approximation is the value that is not exactly but nearly correct.

Unit digit:It is the rightmost digit in a number.